%0 Journal Article %A İnci M. Erhan %D 2007 %J International Journal of Physical and Mathematical Sciences %B World Academy of Science, Engineering and Technology %I Open Science Index 5, 2007 %T An Expansion Method for Schrödinger Equation of Quantum Billiards with Arbitrary Shapes %U https://publications.waset.org/pdf/1846 %V 5 %X A numerical method for solving the time-independent Schrödinger equation of a particle moving freely in a three-dimensional axisymmetric region is developed. The boundary of the region is defined by an arbitrary analytic function. The method uses a coordinate transformation and an expansion in eigenfunctions. The effectiveness is checked and confirmed by applying the method to a particular example, which is a prolate spheroid. %P 255 - 258